If a rotating object has a kinetic energy of 50 J and a moment of inertia of 5 k

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Question: If a rotating object has a kinetic energy of 50 J and a moment of inertia of 5 kg·m², what is its angular velocity?

Options:

Correct Answer: 10 rad/s

Solution:

Using KE = (1/2)Iω², we have 50 J = (1/2)(5 kg·m²)ω², solving gives ω = 10 rad/s.

If a rotating object has a kinetic energy of 50 J and a moment of inertia of 5 kg·m², what is its angular velocity?

If a rotating object has a kinetic energy of 50 J and a moment of inertia of 5 kg·m², what is its angular velocity?

Step 1: Write down the formula for kinetic energy (KE) of a rotating object: KE = (1/2)Iω².
Step 2: Identify the values given in the problem: KE = 50 J and I = 5 kg·m².
Step 3: Substitute the known values into the formula: 50 J = (1/2)(5 kg·m²)ω².
Step 4: Simplify the equation: 50 J = (2.5 kg·m²)ω².
Step 5: To isolate ω², divide both sides by 2.5 kg·m²: ω² = 50 J / 2.5 kg·m².
Step 6: Calculate the right side: ω² = 20 rad²/s².
Step 7: Take the square root of both sides to find ω: ω = √(20 rad²/s²).
Step 8: Calculate the square root: ω = 4.47 rad/s (approximately).
Step 9: Note that the final answer should be rounded or expressed as needed.

Kinetic Energy of Rotating Objects – This concept involves understanding how kinetic energy is calculated for objects in rotational motion, specifically using the formula KE = (1/2)Iω², where I is the moment of inertia and ω is the angular velocity.
Moment of Inertia – This concept refers to the resistance of an object to changes in its rotational motion, which is dependent on the mass distribution relative to the axis of rotation.
Angular Velocity – This concept involves the rate of rotation of an object, measured in radians per second (rad/s), and is derived from the kinetic energy and moment of inertia.